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5.9.2 Format String
The format specification accepted by mpfr_printf
is an extension of the
printf
one. The conversion specification is of the form:
% [flags] [width] [.[precision]] [type] [rounding] conv |
‘flags’, ‘width’, and ‘precision’ have the same meaning as for
the standard printf
(in particular, notice that the ‘precision’ is
related to the number of digits displayed in the base chosen by ‘conv’
and not related to the internal precision of the mpfr_t
variable).
mpfr_printf
accepts the same ‘type’ specifiers as GMP (except the
non-standard and deprecated ‘q’, use ‘ll’ instead), namely the
length modifiers defined in the C standard:
‘h’ short
‘hh’ char
‘j’ intmax_t
oruintmax_t
‘l’ long
orwchar_t
‘ll’ long long
‘L’ long double
‘t’ ptrdiff_t
‘z’ size_t
and the ‘type’ specifiers defined in GMP plus ‘R’ and ‘P’ specific to MPFR (the second column in the table below shows the type of the argument read in the argument list and the kind of ‘conv’ specifier to use after the ‘type’ specifier):
‘F’ mpf_t
, float conversions‘Q’ mpq_t
, integer conversions‘M’ mp_limb_t
, integer conversions‘N’ mp_limb_t
array, integer conversions‘Z’ mpz_t
, integer conversions‘P’ mpfr_prec_t
, integer conversions‘R’ mpfr_t
, float conversions
The ‘type’ specifiers have the same restrictions as those
mentioned in the GMP documentation:
see Section “Formatted Output Strings” in GNU MP.
In particular, the ‘type’ specifiers (except ‘R’ and ‘P’) are
supported only if they are supported by gmp_printf
in your GMP build;
this implies that the standard specifiers, such as ‘t’, must also
be supported by your C library if you want to use them.
The ‘rounding’ field is specific to mpfr_t
arguments and should
not be used with other types.
With conversion specification not involving ‘P’ and ‘R’ types,
mpfr_printf
behaves exactly as gmp_printf
.
The ‘P’ type specifies that a following ‘o’, ‘u’, ‘x’, or
‘X’ conversion specifier applies to a mpfr_prec_t
argument.
It is needed because the mpfr_prec_t
type does not necessarily
correspond to an unsigned int
or any fixed standard type.
The ‘precision’ field specifies the minimum number of digits to
appear. The default ‘precision’ is 1.
For example:
mpfr_t x; mpfr_prec_t p; mpfr_init (x); … p = mpfr_get_prec (x); mpfr_printf ("variable x with %Pu bits", p); |
The ‘R’ type specifies that a following ‘a’, ‘A’, ‘b’,
‘e’, ‘E’, ‘f’, ‘F’, ‘g’, ‘G’, or ‘n’
conversion specifier applies to a mpfr_t
argument.
The ‘R’ type can be followed by a ‘rounding’ specifier denoted by
one of the following characters:
‘U’ round toward plus infinity ‘D’ round toward minus infinity ‘Y’ round away from zero ‘Z’ round toward zero ‘N’ round to nearest ‘*’ rounding mode indicated by the mpfr_rnd_t
argument just before the correspondingmpfr_t
variable.
The default rounding mode is rounding to nearest. The following three examples are equivalent:
mpfr_t x; mpfr_init (x); … mpfr_printf ("%.128Rf", x); mpfr_printf ("%.128RNf", x); mpfr_printf ("%.128R*f", MPFR_RNDN, x); |
Note that the rounding away from zero mode is specified with ‘Y’ because ISO C reserves the ‘A’ specifier for hexadecimal output (see below).
The output ‘conv’ specifiers allowed with mpfr_t
parameter are:
‘a’ ‘A’ hex float, C99 style ‘b’ binary output ‘e’ ‘E’ scientific format float ‘f’ ‘F’ fixed point float ‘g’ ‘G’ fixed or scientific float
The conversion specifier ‘b’ which displays the argument in binary is
specific to mpfr_t
arguments and should not be used with other types.
Other conversion specifiers have the same meaning as for a double
argument.
In case of non-decimal output, only the significand is written in the
specified base, the exponent is always displayed in decimal.
Special values are always displayed as nan
, -inf
, and inf
for ‘a’, ‘b’, ‘e’, ‘f’, and ‘g’ specifiers and
NAN
, -INF
, and INF
for ‘A’, ‘E’, ‘F’, and
‘G’ specifiers.
If the ‘precision’ field is not empty, the mpfr_t
number is
rounded to the given precision in the direction specified by the rounding
mode.
If the precision is zero with rounding to nearest mode and one of the
following ‘conv’ specifiers: ‘a’, ‘A’, ‘b’, ‘e’,
‘E’, tie case is rounded to even when it lies between two consecutive
values at the
wanted precision which have the same exponent, otherwise, it is rounded away
from zero.
For instance, 85 is displayed as "8e+1" and 95 is displayed as "1e+2" with the
format specification "%.0RNe"
.
This also applies when the ‘g’ (resp. ‘G’) conversion specifier uses
the ‘e’ (resp. ‘E’) style.
If the precision is set to a value greater than the maximum value for an
int
, it will be silently reduced down to INT_MAX
.
If the ‘precision’ field is empty (as in %Re
or %.RE
) with
‘conv’ specifier ‘e’ and ‘E’, the number is displayed with
enough digits so that it can be read back exactly, assuming that the input and
output variables have the same precision and that the input and output
rounding modes are both rounding to nearest (as for mpfr_get_str
).
The default precision for an empty ‘precision’ field with ‘conv’
specifiers ‘f’, ‘F’, ‘g’, and ‘G’ is 6.
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